Mathematics 10 — Exercise 4.1 · Q7 (i) g

Full question

Find the inverse function f⁻¹(x) of the following function f(x), stating any restrictions on its domain.

Step-by-step solution

1. Write the output as y. To find the inverse, solve this equation for the original input x.

   $$y=6\times x-18$$

2. Subtract the constant from both sides.

   $$y+18=6\times x$$

3. Divide both sides by the input coefficient.

   $$x=\frac{y+18}{6}$$

4. Interchange the names x and y: the old output is now the inverse input.

   $$\mathrm{f⁻¹}\left(x\right)=\frac{x}{6}+3$$

5. The inverse domain is the original range. Keep any exclusions or nonnegative-input restriction.

   $$\mathrm{ℝ}$$

Answer

The final answer is shown below.